Dispersion Curves with Graphene

Typically, all three eigenvalues of the relative permittivity tensor of a dielectric material have positive real parts. Suppose that dissipation in such a material is small enough to be ignored. Plane waves refracted from air into that material can be classified as either propagating or evanescent. When the air/material interface is periodically corrugated, only a few of the refracted plane waves are of the propagating type, while the number of evanescent refracted plane waves is denumerably infinite.

But if one of the three eigenvalues has a negative real part, then it is possible for the number of propagating refracted plane waves to be denumerably infinite and that of the evanescent refracted plane waves to be finite (and small). In other words, the dispersion curve can change from elliptic to hyperbolic, with consequences that excite electromagnetics researchers.

In a recent paper published in the Journal of Nanophotonics, SPIE members Mohamed A. K. Othman and Filippo Capolino, along with Caner Guclu of the University of California, Irvine theoretically demonstrate that periodically layered graphene-dielectric are capable of exhibiting both types of dispersion curves as well as the transition from one kind to the other, in the far- and the mid-infrared spectral regimes.

The transition can be managed using a quasi-electrostatic biasing field, they report in “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition.”

Plane waves with negative phase velocity (i.e., phase velocity casting a negative projection on the time-averaged Poynting vector) can propagate inside this composite material.

As these phenomena are possible without an underlying resonance, attenuation can be very weak.

Applications to sub-wavelength imaging and high-resolution sensing should make experimentalists very interested in the graphene-dielectric composite multilayers. Othman and his co-authors indicate that as few as 10 periods should suffice. They offer thin layers of graphene interleaved with hexagonal boron nitride layers as candidates.

Read the article in the SPIE Digital Library.

–SPIE Fellow Akhlesh Lakhtakia is editor-in-chief of the Journal of Nanophotonics.

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